• No results found

Benchmarking of COBAYA3 pin-by-pin for VVER

N/A
N/A
Protected

Academic year: 2021

Share "Benchmarking of COBAYA3 pin-by-pin for VVER"

Copied!
13
0
0

Loading.... (view fulltext now)

Full text

(1)

22nd Symposium of AER on VVER Reactor Physics and Reactor Safety Pruhonice, Czech Republic, October 1-5, 2012

BENCHMARKING OF COBAYA3 PIN-BY-PIN FOR VVER

N. Zheleva, J.J.Herrero*, G.Todorova, P.Ivanov, N.Kolev Institute for Nuclear Research and Nuclear Energy, 1784 Sofia, Bulgaria

nonka.zheleva@gmail.com *Universidad Politecnica de Madrid

josejavier.herrero@upm.es

ABSTRACT

This paper presents results of the benchmarking of COBAYA3 pin-by-pin for VVER-1000 obtained in the frame of the EU NURISP project. The 3D lattice solver in COBAYA3 uses transport corrected multi-group diffusion approximation with side-dependent interface discontinuity factors of GET or Selengut Black Box type. The objective of this study is to test the few-group calculation scheme when using structured and unstructured spatial meshes. Unstructured mesh is necessary to model the water gaps between the hexagonal assemblies. The benchmark problems include pin-by-pin calculations of 2D subsets of the core and comparison with APOLLO2 and TRIPOLI4 transport reference solutions. COBAYA3 solutions in 2, 4 and 8 energy groups have been tested. The results show excellent agreement with the reference ones when using side-dependent interface discontinuity factors.

1. INTRODUCTION

COBAYA3 [1]-[7] is a 3D core simulator code for Cartesian and hexagonal geometry, developed by UPM. It includes a nodal solver based on the ACMFD method [1], [5] and a pin-by-pin solver using the fine-mesh finite-difference (FMFD) method. [2], [3], [7]. The current pin-by-pin version [2], [7] solves the time-dependent multi-group diffusion equation corrected by interface discontinuity factors. A nodal acceleration can be used to speed up the full core pin-by-pin solution process.

In the frame of the EU NURESIM [8] and NURISP [9] projects, it has evolved to include capabilities of using multi-parameter cross-section (XS) libraries and interface discontinuity factors (IDF) in table-interpolation and functional-fitting format. The code has been coupled with core thermal-hydraulics [3], [4], [5], [6] for reactor safety analysis. Neighborhood-dependent IDF [10] of GET [11] and Selengut Black Box homogenization (BBH) [12] type can be applied. Parallelized coupled pin-by-pin calculations [3], [4], [6] using alternate dissections have been implemented in Cartesian geometry.

The numerical validation base at the pin level includes a series of computational benchmarks for PWR [13], [14], [15], VVER [16] and BWR [17]. This work presents COBAYA3 calculations of the NURISP VVER lattice benchmark [16] performed by INRNE and UPM. The aim is to test the pin-by-pin solver for homogenized cells in structured and unstructured meshes. A specific objective is to test the APOLLO2.8 [18] generated pin-by-pin XS and IDF, and to assess the impact of the number of broad energy groups.

(2)

In this paper, the benchmark problems are described in Section 2. The utilized pin-by-pin XS calculation schemes [16] are based on the Method of Characteristics (MOC) in APOLLO2 and are summarized in Section 3. Results and conclusions are given in Sections 4 and 5 respectively.

2. TEST PROBLEMS

The considered geometries are 2D subsets of a VVER-1000 core (19-pin clusters, fuel assembly and assembly cluster), as illustrated in Figures 1 and 2.

Figure 1: UOX-GT 19-pin cluster

Figure 2:

a) UOX assembly of 4.23 w/o av. enrichment (246 pins of 4.4w/o and 66 pins of 3.6w/o) b) 7-assembly UOX-CR /UOX-GT cluster of 4.23w/o with UOX-CR in the center

(3)

The NURISP VVER lattice benchmark [16] includes test problems for core simulators in structured and unstructured meshes. The structured mesh cases are 19-pin clusters as used for branch calculations with APOLLO2 to generate multi-parameter pin-by-pin libraries of neighborhood-dependent XS and IDF. The unstructured mesh problems consist of fuel assemblies and assembly clusters with inter-assembly water gaps.

In this study, results for the following test cases are considered: ƒ 19-pin clusters

- UOX-GT: guide tube surrounded by two rings of UOX pins (Figure 1) - UOX-CT: central tube surrounded by UOX pins

- UOX-CR: control rod surrounded by UOX pins ƒ Fuel assemblies

- UOX-GT: uncontrolled assembly - UOX-CR: controlled assembly

ƒ 7-assembly cluster of a central UOX-CR assembly and 6 peripheral UOX-GT assemblies (forming a color set as shown in Figure 2).

The 19-pin clusters are to be calculated for fixed state parameters: 39.8MWd/kgHM, HZP at 574.15K, Dm=740kg/m3, Cb =53ppm.

The UOX-CR assembly is to be calculated for five states listed in Table 1, as usually done for calculation of the reactivity effects.

Table 1: Assembly thermal-hydraulic states to be calculated

Moderator Fuel Cladding Conditions Temp,K Density g/cm3 Temp, K Density g/cm3 Temp, K Density g/cm3 CB ppm

S1: HZP state (ref) 552 0.76665 552 Ref 552 ref 600

S2: Fuel Doppler react 552 0.76665 924 Ref 552 ref 600

S3: Coolant reactivity 574 0.72527 552 Ref 552 ref 600

S4: 100% void 624 0.09610 552 Ref 552 ref 600

S5: Boron reactivity 552 0.76665 552 Ref 552 ref 0

The 7-assembly cluster is of fresh fuel and is to be calculated for fixed state parameters: HZP at 574.15K, Dm=740 kg/m3 and Cb =53ppm.

The task is to calculate the multiplication factor and the pin-by-pin fission reaction rates in comparison with transport reference solutions:

- APOLLO2 MOC 281g /JEFF3.1.1 solutions [16] validated against TRIPOLI4 results - Well converged TRIPOLI4 /JEFF3.1.1 solutions [16] with σ (k) = ± 10-14 pcm TRIPOLI4 [19] is a 3D Monte Carlo code, trademark of CEA.

(4)

The results presented here have been obtained with reflection boundary conditions on the external boundaries and zero buckling. Benchmarking of COBAYA3 pin-by-pin with XS and IDF from multi-parameter libraries obtained through pin-cluster branch calculations with critical buckling is subject of a separate analysis.

3. CROSS-SECTIONS AND INTERFACE DF

Accurate MOC based calculation schemes [16] with APOLLO2, validated against Monte Carlo solutions have been used to generate the pin-by-pin XS and IDF in 2, 4 and 8 energy groups for COBAYA3. Table 2 shows the adopted energy group structure.

Table 2: Broad energy group structure

2 group structure 4 group structure 8 group structure Lower energy cut off (eV)

1 2.2313E+06 2 8.2085E+05 1 3 9.1188E+03 4 1.3007E+02 2 5 3.9279E+00 1 3 6 6.2506E-01 7 1.4572E-01 2 4 8 0.0000E+00

The pin-by-pin XS and IDF for the considered states are cell-position dependent and have been obtained with the CEA2005V4.1.2 library based on JEFF3.1.1, making use of the following modeling assumptions in APOLLO2:

19-pin clusters

- Reference two-step 281g Pij-MOC calculation scheme in APOLLO2 with SHEM [20] energy mesh

- Step MOC (UOX-GT, UOX-CT) or higher-order Linear Surface (LS) MOC [21] (UOX-CR)

- Fine MOC spatial mesh with 4 rings in the fuel, smeared gap-cladding, 3 radial meshes in the moderator, 12 azimuth sectors [16]

- Simplified LS MOC spatial mesh with 4 rings in the fuel, smeared gap-cladding, one ‘ring’ in the moderator and no azimuth sectors

- MOC parameters: tracking step dr=0.008cm, number of azimuth angles Nφ=48, number of polar angles Nψ=3, Bickley quadrature, P3 scattering anisotropy;

LS MOC surface subdivision factor Ndiv=6, threshold size 0.74 cm Fuel assembly

- Reference two-step 281g Pij-MOC calculation scheme in APOLLO2 with SHEM energy mesh

- Step MOC solver

- MOC spatial mesh with 2 rings in the fuel, smeared gap-cladding, 6 azimuth sectors only in CR and peripheral cells, 2566 regions in a whole assembly

(5)

Assembly cluster

- Reference two-step 281g Pij-MOC calculation scheme in APOLLO2 with SHEM energy mesh

- LS MOC solver

- LS MOC spatial mesh with 2 rings in the fuel, smeared gap-cladding, one ‘ring’ and no azimuth sectors in the moderator except for CR cells where 6 azimuth sectors are used; 1070 regions in 1/6 color set

- LS MOC parameters: dr = 0.008, Nφ = 36, Nψ = 2, P1; Ndiv= 6, threshold 0.74 cm The same nuclear data and calculation parameters have been used to obtain the APOLLO2 deterministic reference solutions [16] for the considered cases.

4. RESULTS 4.1 19-pin clusters

This configuration allows the use of structured spatial mesh in COBAYA3. Table 3 summarizes the comparison of COBAYA3 vs. APOLLO2 computed multiplication factors and normalized pin-by-pin fission reaction rates (FRR). The results show that the impact of the number of broad energy groups is small compared to that of the transport correction of homogenization errors. Table 4 shows a comparison with TRIPOLI4 reference solutions.

Table 3: Biases of COBAYA3 vs. APOLLO2 reference results

UOX-GT UOX-CR Code

k-inf Δk(C3-A2) pcm maxΔFRR (C3-A2)*100 k-inf Δk(C3-A2) pcm maxΔFRR (C3-A2)*100

APOLLO2 ref 0.96217 0.61971 C3 2g, no IDF 0.96302 +85 0.22 0.61367 -604 0.11 C3 4g, no IDF 0.96230 +14 0.19 0.60688 -1283 0.06 C3 8g, no IDF 0.96199 -17 0.22 0.60745 -1227 0.11 C3 2g, GET 0.96214 -2 0.02 0.61972 +0.3 0.02 C3 4g, GET 0.96214 -2 0.02 0.61971 -0.2 0.02 C3 8g, GET 0.96214 -2 0.02 0.61971 -0.2 0.02

Table 4: Multiplication factors and biases to TRIPOLI4 reference solution

UOX-GT UOX-CR Code

k-inf Δk, pcm k-inf Δk, pcm

TRIPOLI4 ref 0.96253 ± 11E-5 - 0.61981± 11E-5 -

APOLLO2 LS MOC 281g 0.96216 -37 0.61971 -10

COBAYA3 8g, GET IDF 0.96214 -39 0.61971 -10

Table 5 presents the computed pin fission rates for 1/6 19-pin clusters at 39.8 MWd/kgH. The COBAYA3 results show a perfect reproduction of the APOLLO2 reference solutions when using side- and cell position dependent GET IDF. The solutions with IDF are nearly the same in 2, 4 and 8 energy groups.

(6)

Table 5: COBAYA3 2g vs. APOLLO2 ref solutions for 1/6 pin clusters at 39.8MWd/kgH

UOX-CT UOX-GT UOX-CR Cell N C3 FRR ΔFRR, % C3 FRR ΔFRR, % C3 FRR ΔFRR, % 1 0.991 0.00 0.993 -0.01 1.018 0.02 2 0.992 -0.01 0.994 0.01 1.014 -0.01 3 1.013 0.00 1.010 0.00 0.976 -0.01 4 0.991 0.00 0.993 -0.01 1.018 0.00 5 1.013 0.00 1.010 0.00 0.975 0.00

Figures 3 - 5 illustrate the biases of COBAYA3 to APOLLO2 and TRIPOLI4 computed pin- by-pin fission rate distributions.

Comparison C3 versus A2 -0 4 0 0,01 5 2 GT 0 -0,01 6 3 1

Dev Kinf (A2), pcm 1

Max dev FRR, % 0,0108 Average dev FRR, % 0,01 Kinf A2 Kinf C3 0,96267 0,96268 Comparison C3 versus T4 -0,1 4 0,1 0 5 2 GT 0,1 -0,1 6 3 1 Dev Kinf (T4), pcm 15 Max dev FRR, % 0,08 Average dev FRR, % 0,05 Kinf T4 Kinf C3 0,96253 0,96268 Figure 3: Biases of COBAYA 8g GET to APOLLO2 MOC and TRIPOLI4 ref results

for 19-pin UOX-GT cluster Comparison C3 versus A2 0,00 4 0,00 -0,01 5 2 CT 0,00 0,00 6 3 1

Dev Kinf (A2), pcm 1

Max dev FRR, % 0,0075 Average dev FRR, % 0,00 Kinf A2 Kinf C3 0,98668 0,98668 Comparison C3 versus T4 -0,01 4 0,01 0,02 5 2 CT 0,03 -0,05 6 3 1 Dev Kinf (T4), pcm 20 Max dev FRR, % 0,0461 Average dev FRR, % 0,0234 Kinf T4 Kinf C3 0,98648 0,98668 Figure 4: Biases of COBAYA 8g GET to APOLLO2 MOC and TRIPOLI4 ref results

(7)

Comparison C3 versus A2 Comparison C3 versus T4

0,00 -0,04 4 4 0,00 -0,01 0,25 -0,43 5 2 5 2 CR -0,01 0,02 CR 0,30 -0,08 6 3 1 6 3

Dev Kinf (A2), pcm 0,3 Dev Kinf (T4), pcm -9

Max dev FRR, % 0,02 Max dev FRR, % 0,43

Average dev FRR, % 0,01 Average dev FRR, % 0,22

Kinf A2 0,61971 Kinf T4 0,61981

1

Figure 5: Biases of COBAYA 8g GET to APOLLO2 LS MOC and TRIPOLI4 ref results for 19-pin UOX-CR cluster

4.2 Fuel assembly

A profiled VVER-1000 assembly of 4.23w/o average initial enrichment is considered:

a) UOX-CR assembly at 39.8 MWd/kgHM b) UOX-GT assembly at zero burn-up

In order to model the peripheral water gap, unstructured spatial mesh must be used. Table 6 summarizes the comparison of COBAYA3 vs. APOLLO2 solutions for UOX-CR assembly when using GET discontinuity factors for the interior cells and the irregular peripheral cells.

Table 6: COBAYA3 vs. APOLLO2 results for UOX-CR assembly at 39.8MWd/kgHM

State Code k-inf Δk (C3-A2), pcm max ΔFRR*100

S1 A2 MOC 281g P0* 0,73812 - - COBAYA3 2g GET 0,73827 15 0,27 COBAYA3 4g GET 0,73820 7 0,37 COBAYA3 8g GET 0,73820 8 0,34 S2 A2 MOC 281g P0* 0,73010 - - COBAYA3 2g GET 0,73024 14 0,27 COBAYA3 4g GET 0,73017 7 0,32 COBAYA3 8g GET 0,73017 7 0,35 S3 A2 MOC 281g P0* 0,73062 - - COBAYA3 2g GET 0,73075 13 0,26 COBAYA3 4g GET 0,73067 5 0,33 COBAYA3 8g GET 0,73067 5 0,33 S4 A2 MOC 281g P0* 0,42612 - - COBAYA3 2g GET 0,42612 0 0,03 COBAYA3 4g GET 0,42611 -1 0,03 COBAYA3 8g GET 0,42611 -1 0,04 S5 A2 MOC 281g P0* 0,77432 - - COBAYA3 2g GET 0,77441 9 0,31 COBAYA3 4g GET 0,77433 1 0,36 COBAYA3 8g GET 0,77433 1 0,38

(8)

Good performance of the COBAYA3 pin-by-pin solver across the mesh irregularities is displayed. The results show that:

- the biases of the inside assembly pins are very low, similar to those for structured mesh - the average absolute bias is below 0.05 %

- a single corner pin #1 shows bias of app. 0.3%

Figure 6 illustrates the COBAYA3 2g computed pin-by-pin fission rate distribution for irradiated UOX-CR assembly in State 1 and the biases to APOLLO2 ref solution, if no discontinuity factors are used. The bias in k-infinity is - 973 pcm. The maximum bias in pin fission rates is -1.70 (expressed as ΔFRR*100) for pin #40 near a CR, or -1.82 % for pin #15 (with relative FRR of 0.928) next to a CR.

Figure 7 shows the COBAYA3 2g GET computed pin-by-pin fission rate distribution for the same UOX-CR assembly in State 1 and the biases to APOLLO2 ref solution.

Figure 8 shows the COBAYA3 8g BBH computed pin-by-pin fission rate distribution for a fresh UOX-GT assembly in State 1 and the biases to APOLLO2 ref solution.

2 energy groups, no DF 1,193 1,186 0,69 46 1,220 1,164 1,212 1,155 0,81 0,82 47 37 Max FRR deviation 1,70 1,120 1,188 1,143 Average FRR deviation 0,83 1,123 1,182 1,134 Delta K inf, pcm -973 -0,34 0,66 0,86 48 38 29 1,022 1,086 1,166 1,131 1,037 1,091 1,160 1,122 -1,55 -0,51 0,60 0,89 49 39 30 22 0,862 0,982 1,058 1,153 1,126 0,874 0,999 1,067 1,148 1,117 -1,29 -1,70 -0,89 0,51 0,87 50 40 31 23 16 0,772 0,829 0,917 1,046 1,154 1,131 0,771 0,837 0,933 1,058 1,148 1,122 0,13 -0,84 -1,59 -1,21 0,52 0,88 51 41 32 24 17 11 0,735 0,758 0,000 0,917 1,059 1,166 1,143 0,729 0,753 0,000 0,934 1,068 1,160 1,134 0,59 0,50 0,00 -1,61 -0,90 0,60 0,86 52 42 33 25 18 12 7 0,000 0,737 0,764 0,832 0,983 1,086 1,188 1,164 0,000 0,732 0,759 0,840 1,000 1,092 1,182 1,155 0,00 0,53 0,52 -0,85 -1,69 -0,51 0,67 0,84 53 43 34 26 19 13 8 4 0,755 0,733 0,778 0,780 0,864 1,023 1,120 1,221 1,193 0,745 0,726 0,775 0,779 0,877 1,038 1,124 1,212 1,187 0,97 0,70 0,24 0,12 -1,33 -1,57 -0,35 0,81 0,69 54 44 35 27 20 14 9 5 2 0,833 0,744 0,732 0,750 0,000 0,911 1,075 1,161 1,135 1,197 0,820 0,735 0,726 0,744 0,000 0,928 1,086 1,159 1,127 1,195 0,00 1,27 0,84 0,68 0,61 0,00 -1,69 -1,16 0,14 0,88 0,26 56 55 45 36 28 21 15 10 6 3 1 FRR dev N C3 FRR A2 FRR

Figure 6: Pin-by-pin fission rates and biases (C3 2g no DF - A2ref)*100 for UOX-CR assembly at 39.8 MWd/kgHM, in State 1: HZP at 552K

(9)

2 energy groups, GET DF C3 FRR 1.186 A2 FRR 1.186 FRR dev -0.05 N 46 1.212 1.156 1.212 1.155 -0.01 0.03 47 37 Max FRR deviation 0.27 1.123 1.182 1.135 Average FRR deviation 0.03 1.123 1.182 1.134 Delta K inf, pcm 15 -0.02 0.02 0.07 48 38 29 1.038 1.091 1.160 1.123 1.037 1.091 1.160 1.122 0.00 0.01 0.03 0.09 49 39 30 22 0.874 0.999 1.067 1.149 1.119 0.874 0.999 1.067 1.148 1.117 0.00 0.00 0.03 0.04 0.11 50 40 31 23 16 0.771 0.837 0.933 1.058 1.149 1.123 0.771 0.837 0.933 1.058 1.148 1.122 -0.02 0.00 -0.02 0.03 0.04 0.11 51 41 32 24 17 11 0.729 0.753 0.000 0.934 1.068 1.161 1.135 0.729 0.753 0.000 0.934 1.068 1.160 1.134 -0.03 -0.02 0.00 0.00 0.01 0.05 0.10 52 42 33 25 18 12 7 0.000 0.731 0.759 0.840 1.000 1.092 1.182 1.156 0.000 0.732 0.759 0.840 1.000 1.092 1.182 1.155 0.00 -0.01 -0.02 -0.01 -0.01 0.00 0.02 0.05 53 43 34 26 19 13 8 4 0.745 0.726 0.775 0.778 0.877 1.038 1.123 1.212 1.186 0.745 0.726 0.775 0.779 0.877 1.038 1.124 1.212 1.187 -0.02 -0.02 -0.01 -0.03 -0.02 -0.02 -0.01 -0.01 -0.03 54 44 35 27 20 14 9 5 2 0.820 0.735 0.726 0.744 0.000 0.928 1.086 1.159 1.126 1.192 0.820 0.735 0.726 0.744 0.000 0.928 1.086 1.159 1.127 1.195 -0.01 -0.02 -0.02 -0.01 0.00 -0.01 -0.03 -0.03 -0.06 -0.27 55 45 36 28 21 15 10 6 3 1

Figure 7: Pin-by-pin fission rates and biases (C3 2g GET - A2ref)*100 for UOX-CR assembly at 39.8 MWd/kgHM, in State 1: HZP at 552K

(10)

8 energy groups, BBH DF 0,969 0,969 -0,03 46 1,026 0,956 1,026 0,956 -0,02 0,04 47 37 Max FRR deviation, % 0,28 0,995 1,018 0,950 Average FRR deviation, % 0,02 0,994 1,018 0,950 Delta K inf, pcm 2 0,01 0,02 0,02 48 38 29 1,001 0,993 1,015 0,948 1,001 0,992 1,015 0,948 0,03 0,02 0,03 0,03 49 39 30 22 1,005 1,007 0,996 1,014 0,947 1,005 1,006 0,996 1,014 0,947 0,01 0,02 0,01 0,04 0,02 50 40 31 23 16 1,017 1,009 1,002 0,997 1,014 0,948 1,018 1,009 1,002 0,997 1,013 0,947 0,00 0,00 0,00 0,03 0,04 0,02 51 41 32 24 17 11 1,025 1,019 0,000 1,001 0,996 1,015 0,951 1,025 1,019 0,000 1,001 0,996 1,015 0,950 -0,01 0,00 0,00 0,00 0,02 0,02 0,04 52 42 33 25 18 12 7 0,000 1,023 1,018 1,009 1,006 0,992 1,018 0,956 0,000 1,024 1,019 1,009 1,006 0,992 1,018 0,956 0,00 -0,03 -0,02 -0,01 0,01 0,03 0,03 0,02 53 43 34 26 19 13 8 4 1,038 1,029 1,031 1,014 1,004 1,000 0,995 1,026 0,969 1,038 1,029 1,031 1,014 1,004 1,000 0,994 1,026 0,969 0,00 -0,03 -0,01 0,00 0,01 0,00 0,01 0,00 -0,04 54 44 35 27 20 14 9 5 2 1,048 1,037 1,029 1,019 0,000 0,998 1,000 1,004 0,939 0,963 1,048 1,037 1,030 1,020 0,000 0,998 1,000 1,004 0,939 0,965 -0,02 0,00 -0,04 -0,02 0,00 0,00 0,02 0,01 -0,05 -0,28 55 45 36 28 21 15 10 6 3 1 C3 FRR A2 FRR FRR dev N

Figure 8: Pin-by-pin fission rates and biases (C3 8g BBH - A2ref)*100 for a fresh UOX-GT assembly in State 1: HZP at 552K

(11)

4.3 Color set results

The hexagonal color set consists of a central UOX-CR assembly and 6 halves of peripheral UOX-GT assemblies with 4.23 w/o average enrichment. This is a challenging test problem characterized by radial variation of the enrichment and steep thermal flux gradients near the CR as well as in the water holes (GT, CT) and the inter-assembly water gaps. The modeling of inter-assembly water gaps requires the use of unstructured spatial mesh.

Table 7 shows the biases of COBAYA pin-by-pin to APOLLO2 LS MOC 281g results when using GET discontinuity factors for the interior cells and the irregular inter-assembly cells. Good agreement with the reference results is displayed.

Figure 9 illustrates the deviations of COBAYA3 2g to the reference pin fission rates in 1/6 of the central UOX-CR assembly normalized over the whole color set.

Table 7: Summary of COBAYA3 vs. APOLLO2 LS MOC results with 60o rot. symmetry

APOLLO2 COBAYA3 2g GET Δk(C3-A2), pcm max ΔFRR*100 max ΔFRR*100 Central UOX-CR FA Peripheral UOX-GT 1.30908 1.30892 -16 1.02 1.24 0,88 46 1,02 0,95 47 37 0,95 0,99 0,94 48 38 29 0,86 0,87 0,92 0,92 49 39 30 22 0,69 0,72 0,76 0,85 0,86 50 40 31 23 16 0,56 0,54 0,55 0,63 0,74 0,77 51 41 32 24 17 11 0,53 0,39 0,00 0,45 0,53 0,63 0,66 52 42 33 25 18 12 7 0,00 0,15 0,25 0,32 0,33 0,39 0,50 0,54 53 43 34 26 19 13 8 4 0,53 -0,34 -0,12 0,52 0,24 0,18 0,27 0,36 0,44 54 44 35 27 20 14 9 5 2 0,00 0,45 -0,28 -0,48 0,14 0,00 0,27 0,53 0,78 0,68 0,30 56 55 45 36 28 21 15 10 6 3 1

Figure 9: Central UOX-CR assembly of the color set:

(12)

5. SUMMARY AND CONCLUSIONS The results show that:

ƒ COBAYA3 pin-by-pin successfully performs unstructured mesh calculations with Interface DF

ƒ The transport-corrected diffusion theory solutions for 2D sub-sets of the core with neighborhood-dependent XS and DF are very close to the reference results

ƒ The impact of the number of broad energy groups is small compared to that of the transport correction of homogenization errors

ƒ COBAYA3 pin-by-pin is an accurate and computationally efficient core simulator for hexagonal geometry

The analyzed benchmark solutions prove that the use of side-dependent interface discontinuity factors allows achieving the target pin-by-pin fidelity for safety analysis.

ACKNOWLEDGEMENTS

This work is partially funded by the NURISP project (Contract n° 232124) in the 7th Euratom Framework Program of the European Union.

REFERENCES

1. Aragonés J. M., Ahnert C. et al. “The analytic coarse-mesh finite difference method for multi-group and multidimensional diffusion calculations”, Nuclear Science and Engineering 157, 2007

2. Herrero J.J, Ahnert C., Aragonés J.M., “3D whole core fine-mesh multi-group diffusion calculations by domain decomposition through alternate dissections”. M&C/SNA-2007, Monterey, 2007

3. J.J. Herrero et al, “Performance of whole core pin-by-pin calculations by domain decomposition through alternate dissections in steady state and transient calculations”, Proc.

M&C 2009, Saratoga Springs, NY, May 3-7, 2009

4. Jiménez J., Cuervo D., Aragonés J.M., “A domain decomposition methodology for pin-by-pin coupled neutronic and thermal–hydraulic analyses in COBAYA3“, Nuclear Engineering

and Design, 240, 2010

5. J.A.Lozano, J.Jiménez, N.García-Herranz, J.M. Aragonés, UPM, “Extension of the analytic nodal diffusion solver ANDES to triangular-Z geometry and coupling with COBRA-IIIc for hexagonal core analysis” Annals of Nuclear Energy, 37, 380-388, 2010

6. Jiménez J., Herrero J.J, Cuervo D., Aragonés J.M., “Whole Core Pin-by-Pin Coupled Neutronic-Thermal-hydraulic Steady state and Transient Calculations using COBAYA3 code”, 17th Pacific Basin Nuclear Conference, Cancún, 2010

7. J.J.Herrero, “Multi-scale Core-Cell Advanced Methods in Three-Dimensional geometries and Multi-Groups for Light Water Reactors Calculation”, PhD Thesis UPM, Madrid, 2012

(13)

8. C.Chauliac, J.M.Aragones, D.Bestion, D.G.Cacuci, N.Crouzet, F.P.Weiss “NURESIM - A European Software Platform for Nuclear Reactor Simulation: Multi-scale and multi-physics calculations, sensitivity and uncertainty analysis” Nuclear Engineering and Design, 241 (9), 2010, 3416–3426

9. B.Chanaron, C.Ahnert, D.Bestion, M.Zimmermann, D.Cacuci, N.Crouzet, “The European Project NURISP for Nuclear Reactor Simulation”, Proc. ANS Winter Mtg., Las Vegas, Nevada, 2010

10. Herrero JJ., N.García-Herranz, D.Cuervo, C.Ahnert, “Neighborhood-corrected interface discontinuity factors for multi-group pin-by-pin diffusion calculations for LWR”, Annals of Nuclear Energy, Elsevier, 46 (2012)

11. K.S.Smith, Assembly homogenization techniques for light water reactor analysis,

Progress in Nuclear Energy, 17 (1986) 303

12. R.Sánchez, Assembly homogenization techniques for core calculations, Progress in

Nuclear Energy, 51 (2009) 14-31

13. D.Couyras et al, Specifications of the PWR NURESIM Core Physics Benchmarks. Part 1:

Cell and Lattice Scope, NURESIM Report 17a_T1.4.2_PWR-Cells-Lattice.pdf, June and

October 2006

14. Kozlowski, T., Downar, T., 2003. OECD/NEA and U.S. NRC PWR MOX/UO2 core transient benchmark. Final Specifications, Revision 2, OECD NEA/NSC/DOC (2003)20 15. N.Zheleva, P.Ivanov, N.Mihaylov, N.P.Kolev, Y.Bilodid, U.Rohde, S.Mittag, JJ. Herrero, N.García-Herranz,“Report on the results of PWR benchmarks using COBAYA3 and DYN3D pin-by-pin”, NURISP R-D1.4.4, January and March 2012

16. G.Todorova, N.Zheleva, N.Petrov, P.Ivanov, N.P.Kolev (INRNE), JJ.Herrero (UPM)

“Specifications and results of the VVER lattice benchmark using APOLLO2, TRIPOLI4 and

COBAYA3 pin-by-pin”, NURISP R-D1.4.5a, January and May 2012

17. José J. Herrero, Jan Dufek, Stefano Canepa, “BWR benchmarking results using TRIPOLI4, APOLLO2 and COBAYA3”,NURISP R-D1.4.6, February 2012

18. R. Sanchez et al, “APOLLO2 Year 2010”, Nuclear Engineering and Technology, Vol 42, no. 5, October (2010)

19. TRIPOLI Project Team, “TRIPOLI-4 User Guide”, CEA-R-6169, 2008

20. S.Hfaiedth, A.Santamarina, “Determination of the optimized SHEM mesh for neutron transport calculations” Proc. M&C2005, Avignon, France, September 12-15, 2005

21. S.Santandrea, R.Sanchez, P.Mosca, “A Linear Surface characteristic approximation for neutron transport in unstructured meshes”, Nucl. Sci. Eng. Vol. 160, no.1, Elsevier, Sept 2008, pp. 23-40

References

Related documents

• Send an email, newsletter, thank you, etc., that includes a short story about how a gift to United Way is helping someone in the community.. • visit us online to find stories

Unless otherwise noted, any article is the work of the author and does not necessarily represent the views or opinions of the collective Illinois Real Estate

Leading the data centre industry As multiple award winners for data centre design, we are drawing on our knowledge and experience gained from Powergate phase 1 and of building

Short Between Pin 2 or Pin 3 and Pin 1 with Non-Shorted Conductor Open If Pin 2 or Pin 3 is shorted to Pin 1 on either the input or the output, and the other conductor does not

the UCCJA provides the basis whereby a custody decree can be rec- ognized and enforced by another state in that it addresses the prob- lem of a child custody

This product design is not offered by the H&L Tooth Company at this time.

For each research activity listed below, please tell us if you would allow your child to participate in that type of research activity (circle one answer for each research

➔ 18 foot cable allows you to mount the antenna closer to tire sensors, while keeping the Ez-VIS in the vehicle cab.. Tire